Semilinear degenerate elliptic boundary value problems via critical point theory (Q1936051)

In this paper the author studies a class of semilinear elliptic boundary value problems with degenerate boundary conditions which include as particular cases the Dirichlet and Robin problems. The author uses a variant of the Ljusternik-Schnirelman theory of critical points to prove results on the number of solutions to the problem under consideration. The results of this paper extend some earlier theorems due to Castro-Lazer to the degenerate case in the sense that the author also reduces an infinite dimensional problem to a finite dimensional one and then applies a finite dimensional critical point theory as in [\textit{A. Castro} and \textit{A. C. Lazer}, Ann. Mat. Pura Appl., IV. Ser. 120, 113--137 (1979; Zbl 0426.35038)]. Examples of nonlinear terms satisfying the assumptions are given in the text. All necessary background materials is also provided.